Chapter 14: Q. 11 (page 1106)

Translate $d s$ into terms of $r (t)$ .

Short Answer

Expert verified

The $d s$ in term of $r (t)$ is $d s = ||r' (t)|| d t$

Step by step solution

Step 1. Given Information

Translate $d s$ into terms of data-custom-editor="chemistry" $r (t)$ .

Step 2. Let C be a curve in ℝ3 with a smooth parametrization r(t)=(x(t), y(t), z(t)) for t∈[a,b].

Then the integral of $f (x, y, z)$ along C is

$\int_{C} f (x, y, z) d s = \int_{a}^{b} f (x (t), y (t), z (t)) ||r' (t)|| d t$

After comparing

$d s = ||r' (t)|| d t$

The integral along C is sometimes referred to as the integral with respect to arc length.

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Translate $d s$ into terms of $r (t)$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Let C be a curve in ℝ3 with a smooth parametrization r(t)=(x(t), y(t), z(t)) for t∈[a,b].

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Translate ds into terms of r(t).

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Let C be a curve in ℝ3 with a smooth parametrization r(t)=(x(t), y(t), z(t)) for t∈[a,b].

One App. One Place for Learning.

Most popular questions from this chapter

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Translate $d s$ into terms of $r (t)$ .